Global Utilities

No. 97-15

ESTIMATION IN MULTITYPE EPIDEMICS

Tom Britton
School of Statistical Science

A multitype epidemic model is analysed assuming proportionate mixing between types. Estimation procedures for the susceptibilities and infectivities are derived for three sets of data; complete data meaning the whole epidemic process is observed continuously, the removal processes are observed continuously, and only the final state is observed. Under the assumption of a major outbreak in a population of size n it is shown that, for all three data sets, the susceptibility estimators are always efficient, i.e. consistent with n1/2 rate of convergence. The infectivity estimators are 'in most cases' respectively: efficient, efficient, and unidentifiable. However, if some susceptibilities are equal then the corresponding infectivity estimators are respectively: barely consistent ( (log n)1/2 rate of convergence), not   consistent, and unidentifiable.